The initial agreement that saw Rangnick take over as interim manager at Old Trafford included a clause that he would help shape the club's strategy in an advisory role.
Rangnick was also appointed Austria coach last month and his side will take on Croatia, Denmark and France in the Nations League.
However, Rangnick has decided not to continue with Manchester United.
In his first press conference as Austria boss, Rangnick confirmed he would not stay on at United.
"We have come to the conclusion that it is better for me and the club to concentrate fully on the Austrian national team," he said.
"I cancelled the consultancy contract."
Rangnick, who took charge of the Old Trafford team in December, helped United to a sixth place finish in the Premier League.
The Red Devils eventually appointed Erik ten Hag as first team coach and the club's CEO says they are putting a plan in place that will help the club gain long-term success.
A statement from the club said: "We would like to thank Ralf Rangnick for his efforts as interim manager over the past six months.
"By mutual agreement, Ralf will now focus solely on his new role as manager of the Austria national team and will not therefore be taking up a consultancy role at Old Trafford.
"We would like to wish Ralf the best of luck in this next chapter of his career."
